Question: Simplify the following expression: $r = \dfrac{5}{3a} + \dfrac{8}{7a}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $3a$ and $7a$ $\lcm(3a, 7a) = 21a$ $ r = \dfrac{7}{7} \cdot \dfrac{5}{3a} + \dfrac{3}{3} \cdot \dfrac{8}{7a} $ $r = \dfrac{35}{21a} + \dfrac{24}{21a}$ $r = \dfrac{35 +24}{21a}$ $r = \dfrac{59}{21a}$